A) 2560
B) 2650
C) 3200
D) 1600
Correct Answer: A
Solution :
Let \[{{d}_{1}}\] be the common difference of the A.P. \[{{x}_{1}},{{x}_{2}},.....,\] then \[{{x}_{8}}-{{x}_{3}}=5{{d}_{1}}=12\Rightarrow {{d}_{1}}=\frac{12}{5}=2.4\] \[\Rightarrow {{x}_{5}}={{x}_{3}}+2{{d}_{1}}=8+2\times \frac{12}{5}=12.8\] Let \[{{d}_{2}}\] be the common difference of the other sequence then \[5{{d}_{2}}=\frac{1}{20}-\frac{1}{8}=\frac{-3}{40}\Rightarrow {{d}_{2}}=\frac{-3}{200}\] \[\Rightarrow \frac{1}{{{h}_{10}}}=\frac{1}{{{h}_{7}}}+3{{d}_{2}}=\frac{1}{200}\Rightarrow {{h}_{10}}=200\] \[\Rightarrow {{x}_{5}}\cdot {{h}_{10}}=12.8\times 200=2560\] So option A is the correct answer.You need to login to perform this action.
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